Small dependencies and large actuarial risks

Methods for computing risk measures such as stop-loss premiums tacitly assume independence of the underlying individual risks. From earlier studies it is already known that this assumption can lead to huge errors even when only small dependencies occur. In the present paper a general model is developed, which covers what happens in practice in a realistic way. Moreover, it is also flexible, in the sense that it allows application in practice. Approximations are presented which are both accurate and transparent and the results obtained are illustrated through some explicit examples.